δ expansion of the O(N)xO(N)-invariant φ2χ2 theory

Using the linear δ expansion we calculate the effective potential of the O(N)xO(N)-invariant φ2χ2 theory, in 3 dimensions, to first order in δ. The φa and χa each represent N massless fields in the vector representation of O(N). We find that the optimization equations give rise to two effective potentials. In one of these, the radiative corrections move the theory away from criticality; i.e., a mass term is induced by radiative corrections. In the other case the sole effect of the radiative corrections is to remove the valleys in the effective potential without the introduction of any mass term